Hiwin D1-N Series - Gain Margin and Phase Margin; Nyquist Plot

D1-N Series Servo Drive User Manual Operation Principles
HIWIN MIKROSYSTEM Corp. 3-9
MD17UE01-1906
3.6 Gain margin and phase margin
3.6.1 Nyquist plot
Gain margin (GM) (Unit: db) is the allowable loop gain which can be increased before closed-loop system
becomes unstable. Phase margin (PM) is the allowable phase delay which can be increased before
closed-loop system becomes unstable.
(1) Gain margin
)(
p
jG ω
is the relative distance from where the Nyquist plot intersects with the negative real axis to
(-1, j0).
p
ω
is the phase crossover frequency. In figure 3.6.1.1,
°=∠ 180)(
p
jG ω
. For the transfer
function
)(sG
in a loop system, its gain margin =
GM =
)(log
)(
log
p
p
jG
jG
ω
ω
1010
20
1
20 −=
dB.
From figure 3.6.1.1 and the Nyquist plot, the following conclusion is known.
A. If
)(
ω jG
does not intersect with the negative real axis,
0=)
(
p
jG
ω
and
dBGM ∞
=
.
When the Nyquist plot does not intersect with the negative real axis at any non-zero finite
frequency,
dBGM ∞=
. Theoretically, loop gain can be infinite before instability occurs.
B. If
)
(
ω j
G
intersects with the negative real axis between 0 and -1,
10 << )(
p
jG
ω
and
dBGM 0>
. When the Nyquist plot intersects with the negative real axis between 0 and -1 at
any frequency, the system is stable as loop gain increases.
C. If
)( ω jG
is on (-1, j0),
1=)(
p
jG ω
and
dB
GM 0=
. When
)( ω j
G
is on (-1, j0),
dBGM 0=
. It means the system has reached the boundary of instability. Loop gain must not
be increased anymore.
D. If
)( ω jG
passes (-1, j0),
1>)(
p
jG ω
and
dBGM
0<
. When
)( ω jG
passes (-1, j0),
dBGM 0<
. Loop gain must be decreased to have stable system.